src/math/Polynomial.hpp

 /*
 * Copyright (c) 2005 The University of Notre Dame. All Rights Reserved.
 *
 * The University of Notre Dame grants you ("Licensee") a
 * non-exclusive, royalty free, license to use, modify and
 * redistribute this software in source and binary code form, provided
 * that the following conditions are met:
 *
 * 1. Acknowledgement of the program authors must be made in any
 *    publication of scientific results based in part on use of the
 *    program.  An acceptable form of acknowledgement is citation of
 *    the article in which the program was described (Matthew
 *    A. Meineke, Charles F. Vardeman II, Teng Lin, Christopher
 *    J. Fennell and J. Daniel Gezelter, "OOPSE: An Object-Oriented
 *    Parallel Simulation Engine for Molecular Dynamics,"
 *    J. Comput. Chem. 26, pp. 252-271 (2005))
 *
 * 2. Redistributions of source code must retain the above copyright
 *    notice, this list of conditions and the following disclaimer.
 *
 * 3. Redistributions in binary form must reproduce the above copyright
 *    notice, this list of conditions and the following disclaimer in the
 *    documentation and/or other materials provided with the
 *    distribution.
 *
 * This software is provided "AS IS," without a warranty of any
 * kind. All express or implied conditions, representations and
 * warranties, including any implied warranty of merchantability,
 * fitness for a particular purpose or non-infringement, are hereby
 * excluded.  The University of Notre Dame and its licensors shall not
 * be liable for any damages suffered by licensee as a result of
 * using, modifying or distributing the software or its
 * derivatives. In no event will the University of Notre Dame or its
 * licensors be liable for any lost revenue, profit or data, or for
 * direct, indirect, special, consequential, incidental or punitive
 * damages, however caused and regardless of the theory of liability,
 * arising out of the use of or inability to use software, even if the
 * University of Notre Dame has been advised of the possibility of
 * such damages.
 */
 
/**
 * @file Polynomial.hpp
 * @author    teng lin
 * @date  11/16/2004
 * @version 1.0
 */ 

#ifndef MATH_POLYNOMIAL_HPP
#define MATH_POLYNOMIAL_HPP

#include <iostream>
#include <list>
#include <map>
#include <utility>

namespace oopse {

template<typename ElemType> ElemType pow(ElemType x, int N) {
    ElemType result(1);

    for (int i = 0; i < N; ++i) {
        result *= x;
    }

    return result;
}

/**
 * @class Polynomial Polynomial.hpp "math/Polynomial.hpp"
 * A generic Polynomial class
 */
template<typename ElemType>
class Polynomial {

    public:
        
        typedef int ExponentType;
        typedef ElemType CoefficientType;
        typedef std::map<ExponentType, CoefficientType> PolynomialPairMap;
        typedef typename PolynomialPairMap::iterator iterator;
        typedef typename PolynomialPairMap::const_iterator const_iterator;
        /** 
         * Calculates the value of this Polynomial evaluated at the given x value.
         * @return The value of this Polynomial evaluates at the given x value
         * @param x the value of the independent variable for this Polynomial function
         */
        ElemType evaluate(const ElemType& x) {
            ElemType result = ElemType();
            ExponentType exponent;
            CoefficientType coefficient;
            
            for (iterator i = polyPairMap_.begin(); i != polyPairMap_.end(); ++i) {
                exponent = i->first;
                coefficient = i->second;
                result  += pow(x, exponent) * coefficient;
            }

            return result;
        }

        /**
         * Returns the first derivative of this polynomial.
         * @return the first derivative of this polynomial
         * @param x
         */
        ElemType evaluateDerivative(const ElemType& x) {
            ElemType result = ElemType();
            ExponentType exponent;
            CoefficientType coefficient;
            
            for (iterator i = polyPairMap_.begin(); i != polyPairMap_.end(); ++i) {
                exponent = i->first;
                coefficient = i->second;
                result  += pow(x, exponent - 1) * coefficient * exponent;
            }

            return result;
        }

        /**
         * Set the coefficent of the specified exponent, if the coefficient is already there, it
         * will be overwritten.
         * @param exponent exponent of a term in this Polynomial 
         * @param coefficient multiplier of a term in this Polynomial 
         */
        
        void setCoefficient(int exponent, const ElemType& coefficient) {
            polyPairMap_.insert(PolynomialPairMap::value_type(exponent, coefficient));
        }

        /**
         * Set the coefficent of the specified exponent. If the coefficient is already there,  just add the
         * new coefficient to the old one, otherwise,  just call setCoefficent
         * @param exponent exponent of a term in this Polynomial 
         * @param coefficient multiplier of a term in this Polynomial 
         */
        
        void addCoefficient(int exponent, const ElemType& coefficient) {
            iterator i = polyPairMap_.find(exponent);

            if (i != end()) {
                i->second += coefficient;
            } else {
                setCoefficient(exponent, coefficient);
            }
        }


        /**
         * Returns the coefficient associated with the given power for this Polynomial.
         * @return the coefficient associated with the given power for this Polynomial
         * @exponent exponent of any term in this Polynomial
         */
        ElemType getCoefficient(ExponentType exponent) {
            iterator i = polyPairMap_.find(exponent);

            if (i != end()) {
                return i->second;
            } else {
                return ElemType(0);
            }
        }

        iterator begin() {
            return polyPairMap_.begin();
        }

        const_iterator begin() const{
            return polyPairMap_.begin();
        }
        
        iterator end() {
            return polyPairMap_.end();
        }

        const_iterator end() const{
            return polyPairMap_.end();
        }

        iterator find(ExponentType exponent) {
            return polyPairMap_.find(exponent);
        }

        size_t size() {
            return polyPairMap_.size();
        }
        
    private:
        
        PolynomialPairMap polyPairMap_;
};


/**
 * Generates and returns the product of two given Polynomials.
 * @return A Polynomial containing the product of the two given Polynomial parameters
 */
template<typename ElemType>
Polynomial<ElemType> operator *(const Polynomial<ElemType>& p1, const Polynomial<ElemType>& p2) {
    typename Polynomial<ElemType>::const_iterator i;
    typename Polynomial<ElemType>::const_iterator j;
    Polynomial<ElemType> p;
    
    for (i = p1.begin(); i !=p1.end(); ++i) {
        for (j = p2.begin(); j !=p2.end(); ++j) {
            p.addCoefficient( i->first + j->first, i->second * j->second);
        }
    }

    return p;
}

/**
 * Generates and returns the sum of two given Polynomials.
 * @param p1 the first polynomial
 * @param p2 the second polynomial
 */
template<typename ElemType>
Polynomial<ElemType> operator +(const Polynomial<ElemType>& p1, const Polynomial<ElemType>& p2) {
    Polynomial<ElemType> p(p1);

    typename Polynomial<ElemType>::const_iterator i;

    for (i =  p2.begin(); i  != p2.end(); ++i) {
        p.addCoefficient(i->first, i->second);
    }

    return p;

}

/**
 * Generates and returns the difference of two given Polynomials. 
 * @return
 * @param p1 the first polynomial
 * @param p2 the second polynomial
 */
template<typename ElemType>
Polynomial<ElemType> operator -(const Polynomial<ElemType>& p1, const Polynomial<ElemType>& p2) {
    Polynomial<ElemType> p(p1);

    typename Polynomial<ElemType>::const_iterator i;

    for (i =  p2.begin(); i  != p2.end(); ++i) {
        p.addCoefficient(i->first, -i->second);
    }

    return p;

}

/**
 * Tests if two polynomial have the same exponents
 * @return true if these all of the exponents in these Polynomial are identical
 * @param p1 the first polynomial
 * @param p2 the second polynomial
 * @note this function does not compare the coefficient
 */
template<typename ElemType>
bool equal(const Polynomial<ElemType>& p1, const Polynomial<ElemType>& p2) {

    typename Polynomial<ElemType>::const_iterator i;
    typename Polynomial<ElemType>::const_iterator j;

    if (p1.size() != p2.size() ) {
        return false;
    }
    
    for (i =  p1.begin(), j = p2.begin(); i  != p1.end() && j != p2.end(); ++i, ++j) {
        if (i->first != j->first) {
            return false;
        }
    }

    return true;
}

typedef Polynomial<double> DoublePolynomial;

} //end namespace oopse
#endif //MATH_POLYNOMIAL_HPP
Revision:	246
Committed:	Wed Jan 12 22:41:40 2005 UTC (20 years, 9 months ago) by gezelter
File size:	8967 byte(s)
Log Message:	merging new_design branch into OOPSE-2.0
#	Content
1	/*
2	* Copyright (c) 2005 The University of Notre Dame. All Rights Reserved.
3	*
4	* The University of Notre Dame grants you ("Licensee") a
5	* non-exclusive, royalty free, license to use, modify and
6	* redistribute this software in source and binary code form, provided
7	* that the following conditions are met:
8	*
9	* 1. Acknowledgement of the program authors must be made in any
10	* publication of scientific results based in part on use of the
11	* program. An acceptable form of acknowledgement is citation of
12	* the article in which the program was described (Matthew
13	* A. Meineke, Charles F. Vardeman II, Teng Lin, Christopher
14	* J. Fennell and J. Daniel Gezelter, "OOPSE: An Object-Oriented
15	* Parallel Simulation Engine for Molecular Dynamics,"
16	* J. Comput. Chem. 26, pp. 252-271 (2005))
17	*
18	* 2. Redistributions of source code must retain the above copyright
19	* notice, this list of conditions and the following disclaimer.
20	*
21	* 3. Redistributions in binary form must reproduce the above copyright
22	* notice, this list of conditions and the following disclaimer in the
23	* documentation and/or other materials provided with the
24	* distribution.
25	*
26	* This software is provided "AS IS," without a warranty of any
27	* kind. All express or implied conditions, representations and
28	* warranties, including any implied warranty of merchantability,
29	* fitness for a particular purpose or non-infringement, are hereby
30	* excluded. The University of Notre Dame and its licensors shall not
31	* be liable for any damages suffered by licensee as a result of
32	* using, modifying or distributing the software or its
33	* derivatives. In no event will the University of Notre Dame or its
34	* licensors be liable for any lost revenue, profit or data, or for
35	* direct, indirect, special, consequential, incidental or punitive
36	* damages, however caused and regardless of the theory of liability,
37	* arising out of the use of or inability to use software, even if the
38	* University of Notre Dame has been advised of the possibility of
39	* such damages.
40	*/
41
42	/**
43	* @file Polynomial.hpp
44	* @author teng lin
45	* @date 11/16/2004
46	* @version 1.0
47	*/
48
49	#ifndef MATH_POLYNOMIAL_HPP
50	#define MATH_POLYNOMIAL_HPP
51
52	#include <iostream>
53	#include <list>
54	#include <map>
55	#include <utility>
56
57	namespace oopse {
58
59	template<typename ElemType> ElemType pow(ElemType x, int N) {
60	ElemType result(1);
61
62	for (int i = 0; i < N; ++i) {
63	result *= x;
64	}
65
66	return result;
67	}
68
69	/**
70	* @class Polynomial Polynomial.hpp "math/Polynomial.hpp"
71	* A generic Polynomial class
72	*/
73	template<typename ElemType>
74	class Polynomial {
75
76	public:
77
78	typedef int ExponentType;
79	typedef ElemType CoefficientType;
80	typedef std::map<ExponentType, CoefficientType> PolynomialPairMap;
81	typedef typename PolynomialPairMap::iterator iterator;
82	typedef typename PolynomialPairMap::const_iterator const_iterator;
83	/**
84	* Calculates the value of this Polynomial evaluated at the given x value.
85	* @return The value of this Polynomial evaluates at the given x value
86	* @param x the value of the independent variable for this Polynomial function
87	*/
88	ElemType evaluate(const ElemType& x) {
89	ElemType result = ElemType();
90	ExponentType exponent;
91	CoefficientType coefficient;
92
93	for (iterator i = polyPairMap_.begin(); i != polyPairMap_.end(); ++i) {
94	exponent = i->first;
95	coefficient = i->second;
96	result += pow(x, exponent) * coefficient;
97	}
98
99	return result;
100	}
101
102	/**
103	* Returns the first derivative of this polynomial.
104	* @return the first derivative of this polynomial
105	* @param x
106	*/
107	ElemType evaluateDerivative(const ElemType& x) {
108	ElemType result = ElemType();
109	ExponentType exponent;
110	CoefficientType coefficient;
111
112	for (iterator i = polyPairMap_.begin(); i != polyPairMap_.end(); ++i) {
113	exponent = i->first;
114	coefficient = i->second;
115	result += pow(x, exponent - 1) * coefficient * exponent;
116	}
117
118	return result;
119	}
120
121	/**
122	* Set the coefficent of the specified exponent, if the coefficient is already there, it
123	* will be overwritten.
124	* @param exponent exponent of a term in this Polynomial
125	* @param coefficient multiplier of a term in this Polynomial
126	*/
127
128	void setCoefficient(int exponent, const ElemType& coefficient) {
129	polyPairMap_.insert(PolynomialPairMap::value_type(exponent, coefficient));
130	}
131
132	/**
133	* Set the coefficent of the specified exponent. If the coefficient is already there, just add the
134	* new coefficient to the old one, otherwise, just call setCoefficent
135	* @param exponent exponent of a term in this Polynomial
136	* @param coefficient multiplier of a term in this Polynomial
137	*/
138
139	void addCoefficient(int exponent, const ElemType& coefficient) {
140	iterator i = polyPairMap_.find(exponent);
141
142	if (i != end()) {
143	i->second += coefficient;
144	} else {
145	setCoefficient(exponent, coefficient);
146	}
147	}
148
149
150	/**
151	* Returns the coefficient associated with the given power for this Polynomial.
152	* @return the coefficient associated with the given power for this Polynomial
153	* @exponent exponent of any term in this Polynomial
154	*/
155	ElemType getCoefficient(ExponentType exponent) {
156	iterator i = polyPairMap_.find(exponent);
157
158	if (i != end()) {
159	return i->second;
160	} else {
161	return ElemType(0);
162	}
163	}
164
165	iterator begin() {
166	return polyPairMap_.begin();
167	}
168
169	const_iterator begin() const{
170	return polyPairMap_.begin();
171	}
172
173	iterator end() {
174	return polyPairMap_.end();
175	}
176
177	const_iterator end() const{
178	return polyPairMap_.end();
179	}
180
181	iterator find(ExponentType exponent) {
182	return polyPairMap_.find(exponent);
183	}
184
185	size_t size() {
186	return polyPairMap_.size();
187	}
188
189	private:
190
191	PolynomialPairMap polyPairMap_;
192	};
193
194
195	/**
196	* Generates and returns the product of two given Polynomials.
197	* @return A Polynomial containing the product of the two given Polynomial parameters
198	*/
199	template<typename ElemType>
200	Polynomial<ElemType> operator *(const Polynomial<ElemType>& p1, const Polynomial<ElemType>& p2) {
201	typename Polynomial<ElemType>::const_iterator i;
202	typename Polynomial<ElemType>::const_iterator j;
203	Polynomial<ElemType> p;
204
205	for (i = p1.begin(); i !=p1.end(); ++i) {
206	for (j = p2.begin(); j !=p2.end(); ++j) {
207	p.addCoefficient( i->first + j->first, i->second * j->second);
208	}
209	}
210
211	return p;
212	}
213
214	/**
215	* Generates and returns the sum of two given Polynomials.
216	* @param p1 the first polynomial
217	* @param p2 the second polynomial
218	*/
219	template<typename ElemType>
220	Polynomial<ElemType> operator +(const Polynomial<ElemType>& p1, const Polynomial<ElemType>& p2) {
221	Polynomial<ElemType> p(p1);
222
223	typename Polynomial<ElemType>::const_iterator i;
224
225	for (i = p2.begin(); i != p2.end(); ++i) {
226	p.addCoefficient(i->first, i->second);
227	}
228
229	return p;
230
231	}
232
233	/**
234	* Generates and returns the difference of two given Polynomials.
235	* @return
236	* @param p1 the first polynomial
237	* @param p2 the second polynomial
238	*/
239	template<typename ElemType>
240	Polynomial<ElemType> operator -(const Polynomial<ElemType>& p1, const Polynomial<ElemType>& p2) {
241	Polynomial<ElemType> p(p1);
242
243	typename Polynomial<ElemType>::const_iterator i;
244
245	for (i = p2.begin(); i != p2.end(); ++i) {
246	p.addCoefficient(i->first, -i->second);
247	}
248
249	return p;
250
251	}
252
253	/**
254	* Tests if two polynomial have the same exponents
255	* @return true if these all of the exponents in these Polynomial are identical
256	* @param p1 the first polynomial
257	* @param p2 the second polynomial
258	* @note this function does not compare the coefficient
259	*/
260	template<typename ElemType>
261	bool equal(const Polynomial<ElemType>& p1, const Polynomial<ElemType>& p2) {
262
263	typename Polynomial<ElemType>::const_iterator i;
264	typename Polynomial<ElemType>::const_iterator j;
265
266	if (p1.size() != p2.size() ) {
267	return false;
268	}
269
270	for (i = p1.begin(), j = p2.begin(); i != p1.end() && j != p2.end(); ++i, ++j) {
271	if (i->first != j->first) {
272	return false;
273	}
274	}
275
276	return true;
277	}
278
279	typedef Polynomial<double> DoublePolynomial;
280
281	} //end namespace oopse
282	#endif //MATH_POLYNOMIAL_HPP